Every day, a quality control inspector of high-quality dishes selects a random sample of 100 dishes and carefully inspects each dish for defects. If the inspector finds convincing evidence that the true proportion of
defective dishes is more than 0.10, then the manufacturing process will be shut down for a complete
inspection of the system.
(a) Define the parameter and specify the hypotheses.
(b) Describe the sampling distribution of the sample proportion of defective dishes assuming that the
true proportion of defective dishes is 0.10. Sketch the sampling distribution.
(c) Using a significance level of 10%, what values of p would provide sufficient evidence to reject the
null hypothesis? Identify this rejection region on your sampling distribution from part (b).
(d) Recognizing that the sample mean changes from sample-to-sample and that the null hypothesis may
or may not be true, describe the four outcomes for the conclusion of this inference procedure. Then
describe a consequence for each of these outcomes.